Guides to odds, probability, and simulation
Four short guides that explain the arithmetic behind a market-implied simulation, in the order most readers need it.
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Start here
A market-implied simulation begins with a sportsbook price and ends with a distribution of complete games. Each step in between is ordinary probability. Read these guides in order: turn a price into a probability, remove the sportsbook's margin from a market, see how repeated sampling turns those probabilities into a distribution, then read the distribution without treating any single number as a promise.
All guides
How implied probability works
Convert American and decimal odds into the break-even probability a price encodes, and see why both sides of a market add up to more than 100%.
How to remove vig from a market
Normalize a two-way market into no-vig probabilities, with a worked example and the assumptions behind the proportional method.
Monte Carlo sports simulation, explained
How repeated random sampling turns market probabilities into outcome distributions, why 10,000 runs help, and what simulation cannot prove.
How to read simulation ranges
Medians, modes, percentiles, and central 80% intervals, plus the common mistakes people make when comparing a line with a distribution.
Put the guides to work
Every calculation in these guides can be reproduced with the free odds calculators. To see the same ideas applied to real games, open today's simulated board or a league hub such as the NFL game simulator, the MLB game simulator, or the soccer game simulator. The methodology explains how SimTheGame implements each step, simulation validation covers how the output is checked, and About SimTheGame explains why the product is built this way.